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1

High order sensitivity analysis of a mistuned blisk including intentional mistuning

Pohle L., Tatzko S., Panning-von Scheidt L., Wallaschek J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

353--368

EN

Small deviations between turbine blades exist due to manufacturing tolerances or material inhomogeneities. This effect is called mistuning and usually causes increased vibration amplitudes and also a lower service life expectancy of bladed disks or so called blisks (bladed integrated disk). The major resulting problem is to estimate the maximum amplitude with respect to these deviations. Due to the probability distribution of these deviations, statistical methods are used to predict the maximum amplitude. State of the art is the Monte-Carlo simulation which is based on a high number of randomly re-arranged input parameters. The aim of this paper is to introduce a useful method to calculate the probability distribution of the maximum amplitude of a mistuned blisk with respect to the random input parameters. First, the applied reduction method is presented to initiate the sensitivity analysis. This reduction method enables the calculation of the frequency response function (FRF) of a Finite Element Model (FEM) in a reasonable calculation time. Based on the Taylor series approximation, the sensitivity of the vibration amplitude depending on normally distributed input parameters is calculated and therewith, it is possible to estimate the maximum amplitude. Calculating only a single frequency response function shows a good agreement with the results of over 1000 Monte-Carlo simulations.

2

Multistage coupling - free vibration of mistuned bladed discs

Rządkowski R., Maurin A.

Prace Naukowe Politechniki Warszawskiej. Transport

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2013

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z. 98

565--573

EN

Considered here was the effect of multistage coupling on the dynamics of an aircraft rotor consisting of eight mistuned bladed discs on a drum-disc shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned system has far more intensive multistage coupling than tuned one.

PL

Artykuł stanowi wprowadzenie do analizy dynamiki wirnika silnika odrzutowego zawierającego osiem rozstrojonych, ułopatkowanych tarcz. Każda ułopatkowana tarcza posiadała różną, rzeczywistą liczbę łopatek. W celu wyjaśnienia wpływu wprowadzonego na poszczególnych stopniach turbiny rozstrojenia na powstawanie rezonansów w badanym układzie, obliczono drgania własne wirujących pojedynczych łopatek, ułopatkowanych tarcz oraz całego wirnika wykorzystując metodę elementów skończonych. Zbadane zostały postacie drgań własnych poszczególnych elementów jak i całego modelu biorąc pod uwagę wpływ prędkości obrotowej taki jak usztywnienie pod działaniem siły odśrodkowej. Otrzymane wartości częstotliwości drgań własnych poszczególnych łopatek, ułopatkowanych tarcz, wału oraz całego układu zostały uważnie przebadane pod kątem wykrycia warunków rezonansowych oraz dodatkowych sprzężeń. Stwierdzono, iż rozstrojenie w układzie powoduje zdecydowanie intensywniejsze występowanie sprzężeń w porównaniu z układami nastrojonymi.

3

Multistage coupling of eight mistuned bladed discs on a solid shaft with 1% mistuning

Maurin A., Rządkowski R., Drewczyński M.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 3

309-317

EN

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Free and forced vibrations were examined. In this study, the global rotating mode shapes of flexible mistuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects.

4

Natural frequencies of tuned and mistuned bladed discs on a shaft

Rządkowski R., Drewczyński M., Kubitz L.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 3

275-289

EN

The dynamic behaviour of a rotor consisting of two tuned and mistuned bladed discs on a solid shaft is considered. The effect of the shaft's flexibility on the dynamic characteristics of the bladed discs and the coupling effects between the shaft and bladed disc modes are investigated. Results show clearly the coupling effects in a bladed disc-shaft system. Interference diagrams are developed, from which the dynamic behaviour of a bladed disc can be predicted for varying flexibility relationships between solid shafts and bladed discs. The global rotating mode shapes of flexible tuned and mistuned bladed disc-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening, are accounted for and all the possible couplings between the flexible parts are allowed. Calculated natural frequencies obtained from the blade, the bladed disc and the shaft with two discs are checked to discover resonance conditions and coupling effects. It is shown that blade mistuning strongly affects the interaction between flexible bladed discs and a flexible shaft. This interaction affects the flexible bladed disc modes and is not restricted to the modes with zero, one and two nodal diameters. The torsional frequency of the shaft with two bladed discs is coupled with the zero nodal diameter modes of the single bladed discs. It is shown that including the shaft in the bladed discs model is important from the designer's point of view and may alter the spectrum of frequencies considerably.

5

2D inviscid flutter of the mistuned Fourth and First Standard Configuration

Rządkowski R., Kovalyov A

Transactions of the Institute of Fluid-Flow Machinery

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2003

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nr 112

139--154

EN

The trend in aviation engines with high specific power and, correspondingly, high aerodynamic loads leads to the problem of aeroelastic behaviour of blades not only in compressors and fans, but also in turbines. Investigations of aeroelastic of the blades in dependence of structural mistuning are presented. A numerical calculation method for unsteady aerodynamic characteristics of oscillating blade cascades under the action of unstable loads is based on solution of the coupled fluid-structure problem, in which the aerodynamic and structural dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem, as the interblade phase angle, at which a stability (instability) would occur, is a part of solution. The ideal gas flow around multiple stage passages (with periodicity on the whole annulus) is described by the unsteady 2D Euler equations in conservative form, which are integrated by using the explicit monotonous second order accurate Godunov-Kolgan finite-volume scheme on the moving grid. The blade is modelled by a very simple two degrees of freedom discrete model. In this model cascade performs the torsional and the bending oscillations under the given law. The aeroelastic behaviour of the blades in the unsteady aerodynamic flow is calculated for the mistuned blades assemblies of the Fourth and First Standard Configurations. The computational domain of the unsteady flow can not be restricted to the single blade passage. The results in the time domain analysis show the beneficial influence of the mistuning of the bending mode in comparison to the torsional mode. The dynamic properties of the mistuned systems are dependent on the way of coupling of the blades, whether it is either aerodynamic or mechanical.